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AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES
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 Title & Authors
AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES
Park Jong-Jin; Zhang Yong;
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 Abstract
We prove that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent. We also show that if a homeomorphism f has more than two fixed points on , then f does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfies the shadowing property but not the average shadowing property. This shows that the converse of the theorem 1.1 in [6] is not true.
 Keywords
average shadowing property;-average-pseudo-orbit;shadowing property(pseudo orbit tracing property);-pseudo-orbit;chain recurrent;
 Language
English
 Cited by
1.
SOME PROPERTIES OF THE STRONG CHAIN RECURRENT SET,;;;

대한수학회논문집, 2010. vol.25. 1, pp.97-104 crossref(new window)
2.
VARIOUS SHADOWING PROPERTIES FOR INVERSE LIMIT SYSTEMS,;

충청수학회지, 2016. vol.29. 4, pp.657-661 crossref(new window)
3.
QUASI-ANOSOV DIFFEOMORPHISMS AND VARIOUS SHADOWING PROPERTIES,;

충청수학회지, 2016. vol.29. 4, pp.651-655 crossref(new window)
1.
Diffeomorphisms with C 1-stably average shadowing, Acta Mathematica Sinica, English Series, 2013, 29, 1, 85  crossref(new windwow)
2.
Symplectic diffeomorphisms with limit shadowing, Asian-European Journal of Mathematics, 2017, 10, 02, 1750068  crossref(new windwow)
3.
h–Average-Shadowing Property and Chaos, Journal of Dynamical Systems and Geometric Theories, 2013, 11, 1-2, 39  crossref(new windwow)
4.
On partial shadowing of complete pseudo-orbits, Journal of Mathematical Analysis and Applications, 2014, 411, 1, 454  crossref(new windwow)
5.
On partial shadowing of complete pseudo-orbits, Journal of Mathematical Analysis and Applications, 2013, 404, 1, 47  crossref(new windwow)
6.
Some dynamical properties for free semigroup actions, Stochastics and Dynamics, 2017, 1850032  crossref(new windwow)
7.
Parameterized IFS with the Asymptotic Average Shadowing Property, Qualitative Theory of Dynamical Systems, 2016, 15, 2, 367  crossref(new windwow)
8.
Asymptotic average shadowing property on compact metric spaces, Nonlinear Analysis: Theory, Methods & Applications, 2008, 69, 9, 2857  crossref(new windwow)
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